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Unformatted text preview: Operations Management
Chapter 12 – Chapter Inventory Management Inventory 12 – 1 Outline Global Company Profile: Global Amazon.com Amazon.com Functions of Inventory Types of Inventory Inventory Management ABC Analysis Record Accuracy Cycle Counting Control of Service Inventories
12 – 2 Outline – Continued Inventory Models Independent vs. Dependent Demand Holding, Ordering, and Setup Costs 12 – 3 Outline – Continued Inventory Models for Independent Inventory Demand Demand The Basic Economic Order Quantity The (EOQ) Model (EOQ) Minimizing Costs Reorder Points Production Order Quantity Model Quantity Discount Models
12 – 4 Outline – Continued Probabilistic Models and Safety Stock Other Probabilistic Models FixedPeriod (P) Systems 12 – 5 Learning Objectives
When you complete this chapter you should be able to:
1. 2. 3. Conduct an ABC analysis Explain and use cycle counting Explain and use the EOQ model for Explain independent inventory demand independent 4. Compute a reorder point and safety Compute stock stock 12 – 6 Learning Objectives
When you complete this chapter you should be able to:
1. Apply the production order quantity Apply model model 2. Explain and use the quantity Explain discount model discount 3. Understand service levels and Understand probabilistic inventory models probabilistic 12 – 7 Amazon.com Amazon.com started as a “virtual” Amazon.com retailer – no inventory, no warehouses, no overhead; just computers taking orders to be filled by others by Growth has forced Amazon.com to Growth become a world leader in warehousing and inventory management management
12 – 8 Amazon.com
1. Each order is assigned by computer to the closest distribution center that has the product(s) 2. A “flow meister” at each distribution center assigns work crews 3. Lights indicate products that are to be picked and the light is reset 4. Items are placed in crates on a conveyor. Bar code scanners scan each item 15 times to virtually eliminate errors.
12 – 9 Amazon.com
1. Crates arrive at central point where items Crates are boxed and labeled with new bar code are 2. Gift wrapping is done by hand at 30 Gift packages per hour packages 3. Completed boxes are packed, taped, Completed weighed and labeled before leaving warehouse in a truck warehouse 4. Order arrives at customer within a week 12 – 10 Inventory One of the most expensive assets One of many companies representing as much as 50% of total invested capital capital Operations managers must balance Operations inventory investment and customer service service 12 – 11 Functions of Inventory
1. To decouple or separate various To parts of the production process parts 2. To decouple the firm from To fluctuations in demand and provide a stock of goods that will provide a selection for customers provide 3. To take advantage of quantity To discounts discounts 4. To hedge against inflation
12 – 12 Types of Inventory Raw material Purchased but not processed Workinprocess Undergone some change but not completed A function of cycle time for a product Maintenance/repair/operating (MRO) Necessary to keep machinery and processes Necessary productive productive Finished goods Completed product awaiting shipment
12 – 13 The Material Flow Cycle
Cycle time 95%
Input Wait for inspection Wait to be moved 5%
Output Move Wait in queue Setup Run time for operator time time Figure 12.1
12 – 14 Inventory Management How inventory items can be How classified classified How accurate inventory records How can be maintained can 12 – 15 ABC Analysis Divides inventory into three classes Divides based on annual dollar volume based Class A  high annual dollar volume Class B  medium annual dollar Class volume volume Class C  low annual dollar volume Used to establish policies that focus Used on the few critical parts and not the many trivial ones many
12 – 16
ABC Analysis
Item Stock Number #10286 #11526 #12760 #10867 #10500 30% Percent of Number of Items Stocked 20% Annual Volume (units) 1,000 500 1,550 350 1,000 x Unit Cost = Annual Dollar Volume $ 90,000 77,000 26,350 15,001 12,500 Percent of Annual Dollar Volume 38.8% 33.2% 11.3% 6.4% 5.4% 23% 72% Class $ 90.00 154.00 17.00 42.86 12.50 A A B B B 12 – 17 ABC Analysis
Item Stock Number #12572 #14075 #01036 #01307 #10572 50% Percent of Number of Items Stocked Annual Volume (units) 600 2,000 100 1,200 250 8,550 x Unit Cost = Annual Dollar Volume $ 8,502 1,200 850 504 150 $232,057 Percent of Annual Dollar Volume 3.7% .5% .4% .2% .1% 100.0% 5% Class $ 14.17 .60 8.50 .42 .60 C C C C C 12 – 18 ABC Analysis
Percent of annual dollar usage 80 80 70 70 60 60 50 50 40 40 30 30 20 20 10 10 0 A Items – – – – – – – B Items –     – 10 20 30 40 C Items
      50 60 70 80 90 100
Figure 12.2
12 – 19 Percent of inventory items ABC Analysis Other criteria than annual dollar Other volume may be used volume Anticipated engineering changes Delivery problems Quality problems High unit cost 12 – 20 ABC Analysis Policies employed may include More emphasis on supplier More development for A items development Tighter physical inventory control for Tighter A items items More care in forecasting A items 12 – 21 Record Accuracy Accurate records are a critical Accurate ingredient in production and inventory systems systems Allows organization to focus on what Allows is needed is Necessary to make precise decisions Necessary about ordering, scheduling, and shipping shipping Incoming and outgoing record Incoming keeping must be accurate keeping Stockrooms should be secure
12 – 22 Cycle Counting Items are counted and records updated Items on a periodic basis on Often used with ABC analysis Often to determine cycle to Has several advantages Eliminates shutdowns and interruptions Eliminates annual inventory adjustment Trained personnel audit inventory accuracy Allows causes of errors to be identified and Allows corrected corrected Maintains accurate inventory records
12 – 23 Cycle Counting Example
5,000 items in inventory, 500 A items, 1,750 B items, 2,750 C 5,000 items items Policy is to count A items every month (20 working days), B Policy items every quarter (60 days), and C items every six months (120 days) (120 Item Class A B C Quantity 500 1,750 2,750 Cycle Counting Policy Each month Each quarter Every 6 months Number of Items Counted per Day 500/20 = 25/day 1,750/60 = 29/day 2,750/120 = 23/day 77/day 12 – 24 Control of Service Inventories Can be a critical component Can of profitability of Losses may come from Losses shrinkage or pilferage shrinkage Applicable techniques include
1. Good personnel selection, training, and Good discipline discipline 2. Tight control on incoming shipments 3. Effective control on all goods leaving Effective facility facility
12 – 25 Independent Versus Dependent Demand Independent demand  the Independent demand for item is independent of the demand for any other item in inventory item Dependent demand  the Dependent demand for item is dependent upon the demand for some other item in the inventory other
12 – 26 Holding, Ordering, and Setup Costs Holding costs  the costs of holding Holding or “carrying” inventory over time or Ordering costs  the costs of Ordering placing an order and receiving goods goods Setup costs  cost to prepare a Setup machine or process for manufacturing an order manufacturing
12 – 27 Holding Costs
Category Housing costs (building rent or depreciation, operating costs, taxes, insurance) Material handling costs (equipment lease or depreciation, power, operating cost) Labor cost Investment costs (borrowing costs, taxes, and insurance on inventory) Pilferage, space, and obsolescence Overall carrying cost
Cost (and range) as a Percent of Inventory Value 6% (3  10%) 3% (1  3.5%) 3% (3  5%) 11% (6  24%) 3% (2  5%) 26%
Table 12.1
12 – 28 Holding Costs
Category ng bly dependi3 s. Housing costs (building rent or onsidera depreciation, 6% ( e 10%) at vary c operating costs, taxes, insurance) on, and interest r lding costs , locati Ho ech he business than 15%, some high t . on t Material handling costs (equipment ts greater than 50% 3.5%) 3% (1 rally greater cos lease or Gene depreciation, have holding cost) items power, operating
Labor cost 3% (3  5%) Investment costs (borrowing costs, taxes, and insurance on inventory) Pilferage, space, and obsolescence Overall carrying cost 11% (6  24%) 3% (2  5%) 26% Cost (and range) as a Percent of Inventory Value Table 12.1
12 – 29 Inventory Models for Independent Demand
Need to determine when and how Need much to order much Basic economic order quantity Production order quantity Quantity discount model 12 – 30 Basic EOQ Model
Important assumptions
1. Demand is known, constant, and Demand independent independent 2. Lead time is known and constant 3. Receipt of inventory is instantaneous and Receipt complete complete 4. Quantity discounts are not possible 5. Only variable costs are setup and holding 6. Stockouts can be completely avoided
12 – 31 Inventory Usage Over Time
Order Order quantity = Q (maximum inventory level) level) Minimum Minimum inventory inventory 0 Usage rate Average Average inventory on hand on Q 2 Inventory level Time
Figure 12.3
12 – 32 Minimizing Costs
Objective is to minimize total costs
Curve for total Curve cost of holding and setup and Minimum Minimum total cost total Annual cost Holding cost Holding curve curve Setup (or order) Setup cost curve cost Optimal order Optimal quantity (Q*) quantity Order quantity
12 – 33 Table 11.5 D The EOQ Model setup cost = Q S Annual Q Q* D S H = Number of pieces per order = Optimal number of pieces per order (EOQ) = Annual demand in units for the inventory item = Setup or ordering cost for each order = Holding or carrying cost per unit per year Annual setup cost = (Number of orders placed per year) Annual x (Setup or order cost per order) = = Annual demand Setup or order Setup cost Number of units in each order cost per order D (S) Q
12 – 34 D The EOQ Model setup cost = Q S Annual Q Q* D S H = Number of pieces per order = Optimal number of pieces per order (EOQ) = Annual demand in units for the inventory item = Setup or ordering cost for each order = Holding or carrying cost per unit per year Annual holding cost = Q H 2 Annual holding cost = (Average inventory level) Annual x (Holding cost per unit per year) = = Order quantity (Holding cost per unit per year) 2 Q ( H) 2
12 – 35 D The EOQ Model setup cost = Q S Annual Q Q* D S H = Number of pieces per order = Optimal number of pieces per order (EOQ) = Annual demand in units for the inventory item = Setup or ordering cost for each order = Holding or carrying cost per unit per year Annual holding cost = Q H 2 Optimal order quantity is found when annual setup cost Optimal equals annual holding cost equals D Q S= H Q 2 Solving for Q* 2DS = Q2H Q2 = 2DS/H Q* = Q* 2DS/H
12 – 36 An EOQ Example
Determine optimal number of needles to order D = 1,000 units 1,000 S = $10 per order $10 H = $.50 per unit per year $.50 Q* = Q* = 2DS H 2(1,000)(10) = 0.50 40,000 = 200 units 12 – 37 An EOQ Example
Determine optimal number of needles to order D = 1,000 units Q* = 200 units 1,000 S = $10 per order $10 H = $.50 per unit per year $.50 Expected Expected Demand D number of = N = = Q* Order quantity orders orders 1,000 1,000 N= = 5 orders per year 200 12 – 38 An EOQ Example
Determine optimal number of needles to order D = 1,000 units Q* = 200 units 1,000 S = $10 per order N = 5 orders per year $10 H = $.50 per unit per year $.50 Number of working Number Expected Expected days per year days time between = T = N orders orders T= 250 = 50 days between orders days 5 12 – 39 An EOQ Example
Determine optimal number of needles to order D = 1,000 units Q* = 200 units 1,000 S = $10 per order N = 5 orders per year $10 H = $.50 per unit per year T = 50 days $.50 Total annual cost = Setup cost + Holding cost D Q S+ H Q 2 1,000 200 TC = ($10) + ($.50) TC ($10) 200 2 TC = TC = (5)($10) + (100)($.50) = $50 + $50 = $100 TC (5)($10)
12 – 40 Robust Model The EOQ model is robust It works even if all parameters It and assumptions are not met and The total cost curve is relatively The flat in the area of the EOQ flat 12 – 41 An EOQ Example
Management underestimated demand by 50% D = 1,000 units 1,500 units Q* = 200 units 1,000 1,500 units Q* S = $10 per order N = 5 orders per year $10 H = $.50 per unit per year T = 50 days $.50 D Q TC = S+ H Q 2 1,500 200 TC = ($10) + ($.50) = $75 + $50 = $125 TC ($10) 200 2 Total annual cost increases by only 25%
12 – 42 An EOQ Example
Actual EOQ for new demand is 244.9 units Actual 244.9 D = 1,000 units 1,500 units Q* = 244.9 units 1,000 1,500 units Q* S = $10 per order N = 5 orders per year $10 H = $.50 per unit per year T = 50 days $.50 D Q TC = S+ H Q 2 1,500 244.9 TC = ($10) + ($.50) TC ($10) 244.9 2 TC = $61.24 + $61.24 = $122.48 TC $61.24 Only 2% less than the total cost of $125 when the order quantity was 200
12 – 43 Reorder Points EOQ answers the “how much” question The reorder point (ROP) tells when to The order order Demand Lead Demand Lead time for a ROP = per day new order in days ROP new per =dxL
D d = Number of working days in a year
12 – 44 Reorder Point Curve
Inventory level (units) Q* Slope = units/day = d ROP ROP (units) (units) Figure 12.5 Lead time = L Time (days)
12 – 45 Reorder Point Example
Demand = 8,000 iPods per year Demand 8,000 250 working day year Lead time for orders is 3 working days Lead d= D Number of working days in a year = 8,000/250 = 32 units ROP = d x L = 32 units per day x 3 days = 96 units 96 12 – 46 Production Order Quantity Model Used when inventory builds up Used over a period of time after an order is placed order Used when units are produced Used and sold simultaneously and 12 – 47 Production Order Quantity Model
Inventory level Part of inventory cycle during Part which production (and usage) is taking place is Demand part of cycle Demand with no production with Maximum Maximum inventory inventory t Time
Figure 12.6
12 – 48 Production Order Quantity Model
Q= H= t= Number of pieces per order p = Daily production rate Holding cost per unit per year d = Daily demand/usage rate Length of the production run in days Annual inventory Holding cost Annual Holding = (Average inventory level) x holding cost per unit per year holding per Annual inventory Annual = (Maximum inventory level)/2 level level Maximum Total produced during Maximum = Total inventory level the production run inventory the = pt – dt
12 – 49 – Total used during Total the production run the Production Order Quantity Model
Q= H= t= Number of pieces per order p = Daily production rate Holding cost per unit per year d = Daily demand/usage rate Length of the production run in days – Total used during Total the production run the Maximum Total produced during Maximum = Total inventory level the production run inventory the = pt – dt However, Q = total produced = pt ; thus t = Q/p
Maximum Q Maximum =p inventory level inventory p –d Q p =Q 1– d p d p Holding cost = Holding Maximum inventory level Q (H) = 2 2 1– H
12 – 50 Production Order Quantity Model
Q= H= D= Number of pieces per order Holding cost per unit per year Annual demand p = Daily production rate d = Daily demand/usage rate Setup cost = (D/Q)S Setup Holding cost = Holding
1 1 2 HQ[1  (d/p)] (D/Q)S = 2 HQ[1  (d/p)] 2DS 2 Q= H[1  (d/p)] Q* = p 2DS H[1  (d/p)]
12 – 51 Production Order Quantity Example
D = 1,000 units S = $10 H = $0.50 per unit per year Q* = 2DS H[1  (d/p)] 2(1,000)(10) 0.50[1  (4/8)] = 80,000 p = 8 units per day d = 4 units per day Q* = = 282.8 or 283 hubcaps 282.8 or hubcaps
12 – 52 Production Order Quantity Model
Note: d=4=
D Number of days the plant is in operation = 1,000 250 When annual data are used the equation becomes Q* = 2DS annual demand rate H 1– annual production rate
12 – 53 Quantity Discount Models Reduced prices are often available when Reduced larger quantities are purchased larger Tradeoff is between reduced product cost Tradeoff and increased holding cost and
Total cost = Setup cost + Holding cost + Product cost TC = D Q S+ H + PD Q 2 12 – 54 Quantity Discount Models
A typical quantity discount schedule
Discount Number 1 2 3 Discount Quantity 0 to 999 1,000 to 1,999 2,000 and over Discount (%) no discount 4 5 Discount Price (P) $5.00 $4.80 $4.75
Table 12.2 12 – 55 Quantity Discount Models
Steps in analyzing a quantity discount
1. For each discount, calculate Q* 2. If Q* for a discount doesn’t qualify, If choose the smallest possible order size to get the discount to 3. Compute the total cost for each Q* or Compute adjusted value from Step 2 adjusted 4. Select the Q* that gives the lowest total Select cost cost
12 – 56 Quantity Discount Models
Total cost Total curve for discount 1 discount Total cost curve for discount 2 Total cost $ b a
1st price 1st break break Total cost curve for discount 3 Q* for discount 2 is below the allowable range at point a Q* and must be adjusted upward to 1,000 units at point b and 2nd price 2nd break break 0 1,000 2,000 Order quantity Figure 12.7
12 – 57 Quantity Discount Example
Calculate Q* for every discount Q* = 2DS IP Q1* = Q2* = Q3* = 2(5,000)(49) = 700 cars/order 700 (.2)(5.00) 2(5,000)(49) = 714 cars/order 714 (.2)(4.80) 2(5,000)(49) = 718 cars/order 718 (.2)(4.75)
12 – 58 Quantity Discount Example
Calculate Q* for every discount Q* = 2DS IP Q1* = Q2* = Q3* = 2(5,000)(49) = 700 cars/order 700 (.2)(5.00) 2(5,000)(49) = 714 cars/order 714 (.2)(4.80) 1,000 — adjusted 2(5,000)(49) = 718 cars/order 718 (.2)(4.75) 2,000 — adjusted
12 – 59 Quantity Discount Example
Discount Number 1 2 3 Unit Price $5.00 $4.80 $4.75 Order Quantity 700 1,000 2,000 Annual Product Cost $25,000 $24,000 $23.750 Annual Ordering Cost $350 $245 $122.50 Annual Holding Cost $350 $480 $950 Total $25,700 $24,725 $24,822.50
Table 12.3 Choose the price and quantity that gives Choose the lowest total cost the Buy 1,000 units at $4.80 per unit Buy 1,000 $4.80
12 – 60 Probabilistic Models and Safety Stock Used when demand is not constant or Used certain certain Use safety stock to achieve a desired Use service level and avoid stockouts service ROP = d x L + ss ROP ss
Annual stockout costs = the sum of the units short Annual x the probability x the stockout cost/unit x the number of orders per year the
12 – 61 Safety Stock Example
ROP = 50 units ROP 50 Orders per year = 6 Orders Stockout cost = $40 per frame Stockout $40 Carrying cost = $5 per frame per year $5 Number of Units 30 40 50 60 70 Probability .2 .2 .3 .2 .1 1.0
12 – 62 ROP Safety Stock Example
ROP = 50 units ROP 50 Orders per year = 6 Orders
Safety Stock 20 10 0 Additional Holding Cost (20)($5) = $100 (10)($5) = $ 50 (10)(.1)($40)(6) $ Stockout cost = $40 per frame Stockout $40 Carrying cost = $5 per frame per year $5
Stockout Cost $0 = $240 Total Cost $100 $290 $960 0 (10)(.2)($40)(6) + (20)(.1)($40)(6) = $960 A safety stock of 20 frames gives the lowest total cost safety 20 ROP = 50 + 20 = 70 frames ROP 50
12 – 63 Probabilistic Demand Inventory level Minimum demand during lead time Maximum demand during lead time Mean demand during lead time ROP = 350 + safety stock of 16.5 = 366.5 ROP 350 16.5 ROP ROP Normal distribution probability of Normal demand during lead time demand Expected demand during lead time (350 kits) Expected (350 Safety stock 16.5 units 0
Figure 12.8 Lead Lead time time Time Place Place order order Receive Receive order order
12 – 64 Probabilistic Demand Probability of no stockout 95% of the time Risk of a stockout Risk (5% of area of normal curve) normal Mean Mean demand 350 350 ROP = ? kits Safety Safety stock stock z Quantity 0 Number of Number standard deviations standard
12 – 65 Probabilistic Demand
Use prescribed service levels to set safety Use stock when the cost of stockouts cannot be determined determined ROP = demand during lead time + Zσ dLT
where Z = number of standard number deviations deviations σ dLT = standard deviation of standard demand during lead time demand
12 – 66 Probabilistic Example
Average demand = µ = 350 kits Average Standard deviation of demand during lead time = σ dLT = 10 kits Standard 5% stockout policy (service level = 95%) service 95%) Using Appendix I, for an area under the curve Using of 95%, the Z = 1.65 95%, 1.65 Safety stock = Zσ dLT = 1.65(10) = 16.5 kits Safety 1.65(10) Reorder point = expected demand during lead expected time + safety stock time = 350 kits + 16.5 kits of safety 16.5 stock stock = 366.5 or 367 kits 367 12 – 67 Other Probabilistic Models
When data on demand during lead time is When not available, there are other models available available 1. When demand is variable and lead When time is constant time 2. When lead time is variable and When demand is constant demand 3. When both demand and lead time When are variable are
12 – 68 Other Probabilistic Models
Demand is variable and lead time is constant
ROP = (average daily demand ROP average x lead time in days) + Zσ dLT lead
where σ d = standard deviation of demand per day σ dLT = σ d lead time lead 12 – 69 Probabilistic Example
Average daily demand (normally distributed) = 15 Average Standard deviation = 5 Standard Lead time is constant at 2 days Z for 90% = 1.28 Lead for 90% 1.28 90% service level desired From Appendix I ROP = (15 units x 2 days) + Zσ dlt (15 = 30 + 1.28(5)( 2) = 30 + 9.02 = 39.02 ≈ 39 Safety stock is about 9 iPods Safety
12 – 70 Other Probabilistic Models
Lead time is variable and demand is constant
ROP = (daily demand x ROP daily average lead time in days) average = Z x (daily demand) x σ LT
where σ LT = standard deviation of lead time in days 12 – 71 Probabilistic Example
Daily demand (constant) = 10 Daily Average lead time = 6 days Average Standard deviation of lead time = σ LT = 3 Standard 98% service level desired Z for 98% = 2.055 for 98% 2.055 From Appendix I ROP = (10 units x 6 days) + 2.055(10 units)(3) (10 = 60 + 61.65 = 121.65 Reorder point is about 122 cameras Reorder cameras
12 – 72 Other Probabilistic Models
Both demand and lead time are variable
ROP = (average daily demand ROP average x average lead time) + Zσ dLT average
σd σ LT = = standard deviation of demand per day standard deviation of lead time in days σ dLT = (average lead time x σ d2) average + (average daily demand)2 x σ LT2 12 – 73 Probabilistic Example
Average daily demand (normally distributed) = 150 Average Standard deviation = σ d = 16 Standard Average lead time 5 days (normally distributed) Average Standard deviation = σ LT = 1 day day 95% service level desired Z for 95% = 1.65 for 95% 1.65 From Appendix I ROP = (150 packs x 5 days) + 1.65σ dLT (150 = (150 x 5) + 1.65 (5 days x 162) + (1502 x 12) = 750 + 1.65(154) = 1,004 packs 750 packs 12 – 74 FixedPeriod (P) Systems Orders placed at the end of a fixed period Inventory counted only at end of period Order brings inventory up to target level Only relevant costs are ordering and holding Lead times are known and constant Items are independent from one another 12 – 75 FixedPeriod (P) Systems
Target quantity (T) Target Q4 Onhand inventory Q2 Q1 P P Q3 P Time
Figure 12.9
12 – 76 FixedPeriod (P) Example
3 jackets are back ordered jackets It is time to place an order No jackets are in stock Target value = 50 Target 50 Order amount (Q) = Target (T)  OnOrder hand inventory  Earlier orders not yet hand received + Back orders received Q = 50  0  0 + 3 = 53 jackets 50 12 – 77 FixedPeriod Systems Inventory is only counted at each Inventory review period review May be scheduled at convenient times Appropriate in routine situations May result in stockouts between May periods periods May require increased safety stock 12 – 78 ...
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 Fall '09
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